What kind of problems cannot be solved using machine learning techniques?
At least you should be aware of two points:


P/NP/NP-hard (and all other class of complexities) are thoroughly valid for the machine learning area as well. Because these concepts are related to the fundamental of computations (theory of computation), and machine learning is not an exception here. 
One of the useful concepts in the complexity of the learning problem is the VC dimension, PAC learnability, and their related concepts (such as sample complexity). Although these concepts can't be enough to measure the time complexity, they are useful for finding the learner model's capacity.